Compound Interest Calculator
Use this free compound interest calculator to project the growth of any investment. Enter your starting principal, annual interest rate, time period, and compounding frequency, then add an optional monthly contribution to see how regular deposits accelerate growth. Results include the final balance, total contributions, total interest earned, and a full year-by-year table so you can track every step of the compounding journey.
Results are mathematical estimates based on the inputs you provide and assume a constant interest rate throughout the period. They are not a guarantee of investment performance and should not be treated as financial advice. Consult a qualified financial adviser before making investment decisions.
Everything you need to model investment growth
Six features that cover compound interest calculations without complexity or signups.
Live compound interest formula
Results update as you type using the exact A = P*(1+r/n)^(n*t) formula. No Calculate button needed.
Five compounding frequencies
Compare annually, semi-annually, quarterly, monthly, and daily compounding side by side to see how frequency affects your final balance.
Monthly contribution support
Add a regular monthly deposit and the calculator uses the annuity future value formula to show how contributions stack on top of your principal.
Year-by-year growth table
Toggle a full year-by-year breakdown showing balance, cumulative contributions, and interest earned at the end of every year.
100% private, runs in browser
Every calculation happens in your browser. Your financial figures are never sent to a server, stored, or shared with anyone.
Mobile-friendly layout
Clean responsive design that works on phones, tablets, and desktops so you can plan on any device.
Who uses a compound interest calculator?
Anyone planning for long-term financial growth.
Retirement planning
Model how much a lump-sum investment today could be worth at retirement when you account for decades of compounding and steady monthly contributions.
Savings goals
Set a target balance and work backwards: adjust the principal, rate, and years until the final balance meets your goal, whether that is a house deposit or an emergency fund.
Education funds
Project the future value of a college savings account by entering the current balance, expected return, and years until the child reaches university age.
Comparing investment accounts
Enter the same principal and rate at different compounding frequencies to see the exact dollar difference between an account that compounds monthly versus annually.
Understanding the cost of waiting
Run the calculator twice, once starting today and once with a five-year delay, to see concretely how much postponing an investment costs in forgone interest.
Teaching finance concepts
Students and teachers can use the year-by-year table to visualise the snowball effect of compounding and demonstrate why starting early is the single biggest factor in long-term wealth.
About compound interest
A thorough guide to the formula, the math, and why it matters for your money.
What is compound interest?
Compound interest is interest calculated not just on the original principal but also on all the interest that has already accumulated. Every time interest is added to your balance, the enlarged total becomes the new base for the next calculation. This self-reinforcing cycle means the absolute amount of interest you earn each period keeps growing even if the rate never changes. Albert Einstein is often (perhaps apocryphally) credited with calling compound interest the eighth wonder of the world, and while the attribution is disputed, the sentiment is accurate: given enough time, compounding turns ordinary savings rates into remarkable outcomes.
The compound interest formula explained
The standard formula is A = P * (1 + r/n)^(n*t). Here A is the amount after compounding, P is the starting principal, r is the annual interest rate expressed as a decimal (so 7% becomes 0.07), n is the number of compounding periods per year, and t is the number of years. The key insight is the exponent n*t: because compounding periods multiply, even a small increase in n or t produces a dramatically larger result. This calculator plugs your inputs directly into that formula and updates instantly so you can explore any combination without pencil and paper.
Simple interest versus compound interest
Simple interest is calculated only on the original principal. If you deposit $10,000 at 7% simple interest, you earn $700 in year one, $700 in year two, and $700 in every subsequent year regardless of how the total has grown. Over 20 years you earn $14,000 in interest. With compound interest at the same 7% rate compounded monthly, the same $10,000 grows to about $40,387, meaning $30,387 in interest on the same principal. The difference grows exponentially with time, which is why compound interest is universally preferred for savings and investments.
How compounding frequency affects growth
Compounding frequency determines how often earned interest is added to the principal. With annual compounding, interest is calculated and added once per year. With monthly compounding it is done twelve times, and with daily compounding 365 times. Each additional compounding event gives the recently added interest a chance to earn its own interest sooner, which accelerates growth. The difference between annual and daily compounding on a $10,000 investment at 7% over 10 years is about $38, which is modest. But on a $500,000 balance over 30 years the gap widens to thousands of dollars, so for large balances held for decades the frequency truly matters.
The effect of time on compounding
Time is the most powerful variable in the compound interest formula because of the exponent. Doubling the interest rate roughly doubles the outcome, but doubling the time period much more than doubles it because the exponent grows. A 25-year-old who invests $5,000 at 8% and never adds another dollar will have about $109,000 by age 65. A 35-year-old making the same single investment will have only about $50,500, less than half, despite starting just ten years later. This is why financial advisers stress that starting early is more important than the amount invested or even the rate earned.
Why monthly contributions matter
Most people cannot invest a large lump sum at the start, but they can invest steadily over time. A monthly contribution might seem small compared to a large principal, but each deposit immediately begins compounding. The future value of a series of equal monthly payments is PMT * (((1 + i)^m - 1) / i), where i is the monthly interest rate and m is the number of months. Someone who contributes $200 per month at 7% for 30 years ends up with about $227,000 from those contributions alone, on top of whatever their initial principal grew to. Regular contributions also smooth out market timing risk, which is why this strategy is called dollar-cost averaging in investment contexts.
The Rule of 72
The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate to get the approximate number of years it takes for an investment to double. At 6% the answer is 12 years, at 8% it is 9 years, at 9% it is 8 years. The rule assumes compound interest and is most accurate for rates between 4% and 15%. It slightly underestimates doubling time at very high rates, but for everyday planning it is close enough to be genuinely useful. A variation, the Rule of 114, estimates tripling time, and the Rule of 144 estimates quadrupling time.
APR versus APY: understanding the difference
APR (Annual Percentage Rate) is the stated interest rate before the compounding effect is applied. APY (Annual Percentage Yield) is the effective annual rate after accounting for intra-year compounding. A 6% APR compounded monthly produces an APY of about 6.168% because each month the interest is calculated on an already-enlarged balance. When comparing savings accounts or investment products, always compare APYs rather than APRs, because APY reflects what you actually earn. In this calculator, enter the APR and select the compounding frequency; the resulting final balance already reflects the effective APY growth.
Inflation and real returns
Compound interest calculators show nominal growth, meaning the raw dollar amounts without adjusting for inflation. In the real world, inflation erodes purchasing power over time. If your investment earns 7% per year but inflation runs at 3%, your real return is approximately 4%. For long-term planning it is worth running the calculator twice: once at the nominal rate to see the future dollar balance, and once at the inflation-adjusted rate to see what that balance is worth in today's purchasing power. For a rough estimate, subtract the expected inflation rate from your nominal rate and use that as the input.
Taxes and their effect on compound growth
In most countries, interest income is taxed each year, which interrupts the compounding cycle. If you earn 7% but pay 25% tax on the gains annually, your after-tax return is closer to 5.25%. Over 30 years the difference between 7% compounding untaxed and 5.25% compounding after tax is very large. Tax-advantaged accounts such as 401(k) plans, IRAs, ISAs, and PPFs allow investment gains to compound without annual taxation, which is the principal reason financial planners recommend maximising contributions to such accounts before investing in taxable accounts. This calculator does not model taxes, so treat the output as a pre-tax projection.
How to use the year-by-year table
The year-by-year table shows the balance, cumulative contributions, and cumulative interest at the end of each year. Reading through it makes the compounding effect visible: in the early years the interest column grows slowly, but by the middle and later years it is adding large sums annually even as contributions remain constant. The table is useful for identifying specific milestones, such as the year your balance first crosses a round number, the year interest earned in a single year exceeds your annual contributions, or the year the balance doubles from its starting point. Toggle it open after entering your numbers to explore these landmarks.
Frequently asked questions
If you don't find your question here, ask us directly.
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only earns on the original principal, compound interest grows on itself over time. This snowball effect is the reason long-term investors call it the eighth wonder of the world. The longer money stays invested, the more dramatic the compounding effect becomes, which is why starting early matters so much.
The standard compound interest formula is A = P * (1 + r/n)^(n*t), where A is the final amount, P is the starting principal, r is the annual interest rate expressed as a decimal, n is the number of times interest compounds per year, and t is the time in years. For example, $10,000 at 7% annual interest compounded monthly for 10 years becomes $10,000 * (1 + 0.07/12)^(12*10), which equals roughly $20,097. This calculator uses that exact formula.
Simple interest is calculated only on the original principal, so a $10,000 deposit at 7% earns $700 every year regardless of how long it sits. Compound interest also earns on the accumulated interest, so in year two the interest is calculated on $10,700 rather than $10,000. Over short periods the difference is small, but over decades it becomes enormous. A $10,000 investment at 7% for 30 years earns $21,000 in simple interest but over $66,000 with monthly compounding.
The more frequently interest compounds, the faster your balance grows, because each compounding event adds to the base for the next one. Daily compounding produces slightly more than monthly, which beats quarterly, which beats annual. In practice the difference between monthly and daily compounding is very small for typical savings rates. The bigger lever is the interest rate itself and the amount of time the money is invested. This calculator lets you compare frequencies side by side so you can see the exact dollar difference.
The Rule of 72 is a quick mental shortcut for estimating how long it takes an investment to double. Divide 72 by the annual interest rate and the result is approximately the number of years needed. At 6% per year, money doubles in about 12 years (72 / 6). At 9% it doubles in roughly 8 years. The rule assumes compound interest and works best for rates between 4% and 15%. It slightly underestimates for very high rates, but for everyday planning it is accurate enough to be genuinely useful.
Monthly contributions can be just as powerful as the initial principal, because every new deposit immediately starts earning compound interest. The future value of a stream of equal monthly payments is calculated with the formula PMT * (((1 + i)^m - 1) / i), where i is the monthly interest rate and m is the total number of months. Adding even a modest monthly amount early in the investment horizon can produce tens of thousands of extra dollars over 20 to 30 years. This calculator shows you the exact impact of your contribution amount.
Yes, this calculator is completely free. There is no signup, no account, and nothing to install. All calculations run instantly in your browser, so your financial figures never leave your device. You can change any input and the results update in real time. The year-by-year growth table is also included at no cost and requires no extra steps to view.
The difference between daily and monthly compounding is real but usually small in dollar terms. On a $10,000 principal at 7% over 10 years, monthly compounding produces about $20,097 while daily compounding produces about $20,136, a difference of roughly $39. The gap widens with higher balances, higher rates, and longer time horizons, but for most personal finance scenarios the choice of bank or investment product matters far more than whether it compounds daily or monthly. Use this calculator to run the numbers for your specific situation.
Choosing a realistic rate depends on the investment type. Broad stock market index funds have historically returned around 7% to 10% per year on average before inflation, though individual years vary widely. High-yield savings accounts often pay 4% to 5% in high-interest-rate environments but less at other times. Bonds typically return less than stocks over the long run. For a conservative planning estimate, many financial planners suggest 6% to 7% for a diversified portfolio. This calculator is a mathematical tool and does not guarantee any rate of return.
The time to double your money depends on the interest rate and compounding frequency. Using the Rule of 72, divide 72 by your annual rate: at 6% it takes about 12 years, at 8% about 9 years, and at 10% about 7.2 years. For a precise answer, use this calculator: enter your principal, set the final balance target to double the principal, and adjust the years until the output matches. Alternatively, the exact formula is t = ln(2) / (n * ln(1 + r/n)).
No. This calculator produces mathematical projections based on the inputs you enter. Real-world investment returns fluctuate year to year, interest rates on savings accounts change, and inflation reduces the purchasing power of future balances. The results are estimates for planning purposes only and should not be treated as a guarantee of investment performance. For decisions involving significant sums, consult a qualified financial adviser.
The calculator uses the standard compound interest formula A = P * (1 + r/n)^(n*t) for the principal and the annuity future value formula for monthly contributions, which are the same formulas used in textbooks and financial software. Results are accurate to the cent for the inputs given. The year-by-year table applies the same formulas annually so each row is consistent with the final totals. Rounding to whole dollars in the display is the only simplification, and the underlying calculation retains full precision.
APR (Annual Percentage Rate) is the stated interest rate before compounding is applied. APY (Annual Percentage Yield) is the effective rate after accounting for how often interest compounds within the year. A 6% APR compounded monthly has an APY of about 6.168%, because each month the interest is added to the principal before the next calculation. Banks are required to disclose APY on deposit accounts in the United States so you can compare products fairly. Enter the APR in this calculator and choose your compounding frequency to see the effective growth, which reflects the APY.
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